Results 31 to 40 of about 1,758 (174)
Continuous and Lp estimates for the complex Monge-Ampère equation on bounded domains in ℂn
International Journal of Mathematics and Mathematical Sciences, 2002 Continuous solutions with continuous data and Lp solutions with Lp data are obtained for the complex Monge-Ampère equation on bounded domains, without requiring any smoothness of the domains.
Patrick W. Darko
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Application of isotropic geometry to the solution of the Monge–Ampere equation
Қарағанды университетінің хабаршысы. Математика сериясыThis paper explores the Monge–Ampere equation in the context of isotropic geometry. The study begins with an overview of the fundamental properties of isotropic space, including its scalar product, distance formula, and the nature of surfaces and ...
Sh.Sh. Ismoilov
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A curvature flow to the Lp Minkowski-type problem of q-capacity
Advanced Nonlinear Studies, 2023 This article concerns the Lp{L}_{p} Minkowski problem for q-capacity.
Liu Xinying, Sheng Weimin
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Hyperbolic Monge-Ampère Equation
, 2006 In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses,
Howard, Tamani M.
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Simplified Geometric Approach to Freeform Beam Shaper Design
International Journal of Optics, 2020 Beam of light shaping process can be considered ultimate, if both irradiance and wavefront spatial distributions are under control and both can be shaped arbitrarily.
Jacek Wojtanowski, Tadeusz Drozd
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Cubo, 2022 We investigate Monge-Amp\`ere type equations on almost Hermitian manifolds and show an \textit{a priori} $L^\infty$ estimate for a smooth solution of these equations.
Masaya Kawamura
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, 2016 Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity ...
Gutiérrez, Cristian E
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The Monge-Ampère Equation for Freeform Optics
, 2015 The freeform shape of an optical surface is governed by the Monge-Ampère equation coupled with the transport boundary condition.
W.L. IJzerman +7 more
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A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds
Journal of Applied Mathematics, 2013 We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function.
Qiang Ru
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Quasibounded solutions to the complex Monge–Ampère equation
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract We study the Dirichlet problem for the complex Monge–Ampère operator on B‐regular domains in Cn$\mathbb {C}^n$, allowing boundary data that is singular or unbounded. We extend the concept of pluri‐quasibounded functions on the domain to functions on the boundary, defined by the existence of plurisuperharmonic majorants that dominate their ...
Mårten Nilsson
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